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In this paper, we investigate resource allocation in MIMO interference systems where multiple MIMO links share the same frequency band and interfere with each other. For MIMO transmission scheme, we consider a spatial multiplexing scheme that uses linear precoder and decoder. We impose the SINR constraint that the received SINR of each data sub-stream should be larger than a predetermined threshold, and the QoS constraint that the data throughput of individual link should be larger than a required level. In this system, a trade-off exists between the data throughput and the power consumption due to the co-channel interference among the multiple MIMO links. So we arrange a new resource allocation algorithm such that the data throughput and the power consumption are balanced and the QoS constraint is met for each link. We model the resource allocation problem as a noncooperative game and devise a distributed resource allocation algorithm in which the constituent links find a Nash equilibrium point without coordination. The proposed algorithm turns out to perform close to the optimal point achieved by centralized optimization.